RUSSIAN TRANSLATIONS SERIES 1. K.Ya. Kondrat’ev et al. (editors): USSRjUSA Bering Sea Experiment 2. D.V. Nalivkin: Hurricanes, Storms and Tornadoes 3. V.M. Novikov (editor): Handbook of Fishery Technology, Volume 1 4. F.G. Martyshev: Pond Fisheries 5. R.N. Burukovskii: Key of Shrimps and Lobsters 6. V.M. Novikov (editor): Handbook of Fishery Technology, Volume 4 7. V.P. Bykov (editor): Marine Fishes 8. N.N. Tsvelev: Grasses of the Soviet Union 9. L.V. Metlitskii et al.: Controlled Atmosphere Storage of Fruits 10. M.L. Glazovskaya: Soils of the World (2 volumes) 11. V.G. Kort & V.S. Samoilenko: Atlantic Hydrophysical Polygon-70 12. M.A. Mardzhanishvili: Seismic Design of Frame-panel Buildings and Their Structural Members 13. E’.A. Sokolenko (editor): Water and Salt Regimes of Soils: Modeling and Management 14. A.P. Bocharov: A Description of Devices Used in the Study of Wind Erosion of Soils 15. E.S. Artsybashev: Forest Fires and Their Control 16. R.Kh. Makasheva: The Pea 17. N.G. Kondrashova: Shipboard Refrigeration and Fish Processing Equipment 18. S.M. Uspenskii: Life in High Latitudes 19. A.V. Rozova: Biostratigraphic Zoning and Trilobites of the Upper Cambrian and Lower Ordovician of the Northwestern Siberian Platform 20. N.I. Barkov: Ice Shelves of Antarctica 21. V.P. Averkiev: Shipboard Fish Scouting and Electronavigational Equipment 22. D.F. Petrov (Editor-in-Chief): Apomixis and 1st Role in Evolution and Breeding 23. G.A. Mchedlidze: General Features of the Paleobiological Evolution of Cetacea 24. M.G. Ravich et al.: Geological Structure of Mac. Robertson Land (East Antarctica) 25. L.A. Timokhov (editor): Dynamics of Ice Cover 26. K.Ya. Kondrat’ev: Changes in Global Climate 27. P.S. Nartov: Disk Soil-Working Implements 28. V.L. Kontrimavichus (Editor-in-Chief): Beringia in the Cenozoic Era 29. S.V. Nerpin & A.F. Chudnovskii: Heat and Mass Transfer in the Plant-Soil-Air System 30. T.V. Alekseeva et al. : Highway Machines 31. N.I. Klenin et al.: Agricultural Machines 32. V.K. Rudnev: Digging of Soils by Earthmovers with Powered Parts 33. A.N. Zelenin et al.: Machines for Moving the Earth 34. Systematics Breeding and Seed Production of Potatoes 35. D.S. Orlov: Humus Acids of Soils 36. M.M. Severnev (editor): Wear of Agricultural Machine Parts 37. Kh.A. Khachatryan: Operation of Soil-Working Implements in Hilly Regions 38. L.V. Gyachev: Theory of Surface of Plow Bottoms 39. S.V. Kardashevskii et al.: Testing of Agricultural Technological Processes 40. M.A. Sadovskii (editor): Physics of the Earthquake Focus 41. I.M. Dolgin: Climate of Antarctica 42. V.V. Egorov et al: Classification and Diagnostics of Soils of the USSR 43. V.A. Moshkin: Castor RUSSIAN TRANSLATION SERIES (Contd.) 44. E\T. Sarukhanyan: Structure and Variability of the Antarctic Circumpolar Current 45. V.A. Shapa (Chief editor): Biological Plant Protection 46. A.I. Zakharova: Estimation of Seismicity Parameters Using a Computer 47. M.A. Mardzhanishvili & L.M. Mardzhanishvili: Theoretical and Experimental Analysis of Members of Earthquake-proof Frame-panel Buildings 48. S.G Shul’man: Seismic Pressure of Water on Hydraulic Structures 49. Yu. A. Ibad-zade: Movement of Sediments in Open Channels 50. I.S. Popushoi (Chief editor): Biological and Chemical Methods of Plant Protection 51. K.V. Novozhilov (Chief editor): Microbiological Methods for Biological Control of Pests of Agricultural Crops 52. K.I. Rossinskii (editor): Dynamics and Thermal Regimes of Rivers 53. K.V. Gnedin: Operating Conditions and Hydraulics of Horizontal Settling Tanks 54. G.A. Zakladnoi & V.F. Ratanova: Stored-grain Pests and Their Control 55. Ts.E. Mirtskhulava: Reliability of Hydro-reclamation Installations 56. Ia.S. Ageikin: Off-the-road Mobility of Automobiles 57. A.A. Kmito & Yu.A. Sklyarov: Pyrheliometry 58. N.S. Motsonelidze: Stability and Seismic Resistance of Buttress Dams 59. Ia.S. Ageikin: Off-the-road Wheeled and Combined Traction Devices 60. Iu.N. Fadeev & K.V. Novozhilov: Integrated Plant Protection 61. N.A. Izyumova: Parasitic Fauna of Reservoir Fishes of the USSR and Its Evolution 62. O.A. Skarlato (Editor-in-Chief): Investigation of Monogeneans in the USSR 63. A.I. Ivanov: Alfalfa 64. Z.S. Bronshtein: Fresh-water Ostracoda 65. M.G. Chukhrii: An Atlas of the Ultrastructure of Viruses of Lepidopteran Pests of Plants 66. E.S. Bosoi et a!.: Theory, Construction and Calculations of Agricultural Machines, Volume 1 67. G.A. Avsyuk (Editor-in-Chief): Data of Glaciological Studies 68. G.A. Mchedlidze: Fossil Cetacea of the Caucasus 69. A.M. Akramkhodzhaev: Geology and Exploration of Oil- and Gas-bearing Ancient Deltas 70. N.M. Berezina & D.A. Kaushanskii: Presowing Irradiation of Plant Seeds 71. G.U. Lindberg & Z.V. Krasyukova: Fishes of the Sea of Japan and the Adjacent Areas of the Sea of Okhotsk and the Yellow Sea 72. N.I. Plotnikov & 1.1. Roginets: Hydrogeology of Ore Deposits 73. A.V. Balushkin: Morphological Bases of the Systematics and Phylogeny of the Nototheniid Fishes 74. E.Z. Pozin et al.: Coal Cutting by Winning Machines 75. S.S. ShuFman: Myxosporidia of the USSR 76. G.N. Gogonenkov: Seismic Prospecting for Sedimentary Formations 77. I.M. Batugina & I.M. Petukhov: Geodynamic Toning of Mineral Deposits for Planning and Exploitation of Mines 78. 1.1. Abramovich & I.G. Klushin: Geodynamics and Metallogeny of Folded Belts 79. M.V. Mina: Microevolution of Fishes 80. K.V. Konyaev: Spectral Analysis of Physical Oceanographic Data 81. 1.1. Tseitlin & A. A. Kusainov: Role of Internal Friction in Dynamic Analysis of Structures 82. E.A. Kozlov: Migration in Seismic Prospecting MIGRATION IN SEISMIC PROSPECTING MIGRATION IN SEISMIC PROSPECTING E.A. KOZLOV RUSSIAN TRANSLATION SERIES 82 Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business A BALKEMA BOOK Published by: CRCPress/Balkema P.O. Box 447, 2300 AK Leiden, The Netherlands e-mail: [email protected] www.crcpress.com - www.taylorandfrancis.com © 1990 by Taylor & Francis Group, LLC CRC Press/Balkema is an imprint of the Taylor & Francis Group, an iriforma business No claim to original U.S. Government works ISBN 13: 978-90-6191-908-7 (hbk) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www. copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Translation of: Migratsionnie preobrazovaniya v seismorazvedke, Nedra, Moscow, 1986. The author revised and updated the manuscript of the English Edition in 1989. Translator B.B. Bhattacharya Technical Editor S.H. Rao Language Editor Margaret Majithia The translation was checked by the author, Dr. E.A. Kozlov. PREFACE TO ENGLISH TRANSLATION This book first attempts to formulate the problem of 'migration’ as a method applied in seismic prospecting and then to comprehend the unifying fundamentals of the numerous and various migration techniques now in use. Guidelines are offered for the practical implementation of this method in complex structural as well as stratigraphic environment and the short- comings and limitations that ought to be kept in mind when accomplishing migration or interpreting the resultant data are discussed. Hopefully, the book will prove of use not only to practising professionals engaged in designing or running migration procedures, but also to those who would rather deal with the results of migration. The book is not entirely my personal creation. Significant contributions were made, either in the form of discussions on unclear aspects or by direct participation in developing certain algorithms, by A.S. Alekseev, Yu.V. Timoshin, A.K. Urupov, S.A. Vasil’ev, V.M. Glogovskii, I.A. Mushin, V.I. Meshbei, as well as N.M. Tsyplakova and E.Yu. Arkhipova. I thank them sincerely for their assistance. I also thank Dr. B.B. Bhattacharya for his fine translation of this work into English. September 1989 E.A. Kozlov CONTENTS INTRODUCTION 1 CHAPTER 1. THE PRINCIPLES OF MIGRATION 6 1.1 Wave Equation 7 1.2 Interaction of Incident and Reflected Waves 13 1.3 Kirchhoff’s Integral 15 1.4 Wavefield Continuation on the Basis of Analytical Integral Solutions of Wave Equations 17 1.5 Wavefield Continuation by Finite-Difference Solution of the Wave Equation 28 1.6 Models of the Medium and the Seismic Field; Formulation of the Problem of Migration 35 CHAPTER 2. MIGRATION IN THE SPACE-TIME DOMAIN 44 2.1 Forward Wavefield Continuation 44 2.2 Inverse Wavefield Continuation 57 2.3 Features of Migration Based on Integral Transforms in the x, /-Domain 70 2.4 Finite-Difference Migration in the x, /-Domain 82 CHAPTER 3. MIGRATION IN THE FREQUENCY DOMAIN 107 3.1 Migration in kx, «^-Domain 107 3.2 Migration in the kXi /-Domain 121 3.3 Migration in x, ^-Domain 125 CHAPTER 4. OPTIMISED AND NON-LINEAR MIGRATION 128 4.1 Ideal and Regularised Migration Filters 128 4.2 Migration in the Presence of Noise: Unordered Medium 132 4.3 Migration in the Presence of Noise: Ordered Medium 141 vii